Solve 5/7+(1-3/7)*11/3div22/3

$$\frac{ 5 }{ 7 } +(1- \frac{ 3 }{ 7 } ) \times 1 \frac{ 1 }{ 3 } \div 2 \frac{ 2 }{ 3 }$$

Evaluate

$$1$$

Solution Steps

Convert 1 to fraction \frac{7}{7}.

$$\frac{5}{7}+\frac{\left(\frac{7}{7}-\frac{3}{7}\right)\times \frac{1\times 3+1}{3}}{\frac{2\times 3+2}{3}}$$

Since \frac{7}{7} and \frac{3}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{7}+\frac{\frac{7-3}{7}\times \frac{1\times 3+1}{3}}{\frac{2\times 3+2}{3}}$$

Subtract 3 from 7 to get 4.

$$\frac{5}{7}+\frac{\frac{4}{7}\times \frac{1\times 3+1}{3}}{\frac{2\times 3+2}{3}}$$

Multiply 1 and 3 to get 3.

$$\frac{5}{7}+\frac{\frac{4}{7}\times \frac{3+1}{3}}{\frac{2\times 3+2}{3}}$$

Add 3 and 1 to get 4.

$$\frac{5}{7}+\frac{\frac{4}{7}\times \frac{4}{3}}{\frac{2\times 3+2}{3}}$$

Multiply \frac{4}{7} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{7}+\frac{\frac{4\times 4}{7\times 3}}{\frac{2\times 3+2}{3}}$$

Do the multiplications in the fraction \frac{4\times 4}{7\times 3}.

$$\frac{5}{7}+\frac{\frac{16}{21}}{\frac{2\times 3+2}{3}}$$

Multiply 2 and 3 to get 6.

$$\frac{5}{7}+\frac{\frac{16}{21}}{\frac{6+2}{3}}$$

Add 6 and 2 to get 8.

$$\frac{5}{7}+\frac{\frac{16}{21}}{\frac{8}{3}}$$

Divide \frac{16}{21} by \frac{8}{3} by multiplying \frac{16}{21} by the reciprocal of \frac{8}{3}.

$$\frac{5}{7}+\frac{16}{21}\times \frac{3}{8}$$

Multiply \frac{16}{21} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{7}+\frac{16\times 3}{21\times 8}$$

Do the multiplications in the fraction \frac{16\times 3}{21\times 8}.

$$\frac{5}{7}+\frac{48}{168}$$

Reduce the fraction \frac{48}{168} to lowest terms by extracting and canceling out 24.

$$\frac{5}{7}+\frac{2}{7}$$

Since \frac{5}{7} and \frac{2}{7} have the same denominator, add them by adding their numerators.

$$\frac{5+2}{7}$$

Add 5 and 2 to get 7.

$$\frac{7}{7}$$

Divide 7 by 7 to get 1.

$$1$$

Factor

$$1$$